Question 7 of 57

A bar magnet has total length $2 l=20$ units and the field point $P$ is at a distance $\mathrm{d}=10$ units from the centre of the magnet. If the relative uncertainty of length measurement is $1 \%$, then uncertainty of the magnetic field at point P is :

A$4 \%$B$15 \%$C$5 \%$D$10 \%$

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Answer: (A) $4 \%$

Magnetic field at $P, B=\frac{\mu_0}{4 \pi} \frac{m(2 l)}{r^3}$, where $m$ is the pole strength
$\begin{aligned}
\Rightarrow\left(\frac{\Delta B}{B} \times 100\right) & =\left(\frac{\Delta l}{l}\right) \times 100+3\left|\frac{\Delta r}{r}\right| \times 100 \\
& =1 \%+3 \%=4 \%
\end{aligned}$